# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 13 sizeConstants = 24 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "t in component environment (s)" legend_constants[0] = "kf1 in component EGF_EGFRtoEGFEGFR (per_um_s)" legend_constants[1] = "kb1 in component EGF_EGFRtoEGFEGFR (per_s)" legend_constants[2] = "kf2 in component EGF_EGFRtoEGFEGFR (per_s)" legend_constants[3] = "kb2 in component EGF_EGFRtoEGFEGFR (per_s)" legend_states[0] = "EGF in component EGF_EGFRtoEGFEGFR (um)" legend_states[1] = "EGFR in component EGF_EGFRtoEGFEGFR (um)" legend_states[2] = "EGF_EGFR in component EGF_EGFRtoEGFEGFR (um)" legend_states[3] = "EGF_EGFR_INTERNAL in component EGF_EGFRtoEGFEGFR (um)" legend_constants[4] = "km3 in component SHCtoSHCStar (um)" legend_constants[5] = "kf4 in component SHCtoSHCStar (per_s)" legend_constants[6] = "kb4 in component SHCtoSHCStar (per_s)" legend_constants[7] = "kf5 in component SHCtoSHCStar (per_um_s)" legend_constants[8] = "kb5 in component SHCtoSHCStar (per_s)" legend_constants[9] = "kf6 in component SHCtoSHCStar (per_um_s)" legend_constants[10] = "kb6 in component SHCtoSHCStar (per_s)" legend_constants[11] = "kf8 in component SHCtoSHCStar (per_s)" legend_constants[12] = "kb8 in component SHCtoSHCStar (per_s)" legend_constants[13] = "kf10 in component SHCtoSHCStar (per_um_s)" legend_constants[14] = "kb10 in component SHCtoSHCStar (per_s)" legend_constants[15] = "km7 in component SHCtoSHCStar (um)" legend_constants[16] = "km9 in component SHCtoSHCStar (um)" legend_constants[17] = "Vmax7 in component SHCtoSHCStar (per_s)" legend_constants[18] = "Vmax3 in component SHCtoSHCStar (per_s)" legend_constants[19] = "Vmax9 in component SHCtoSHCStar (per_s)" legend_states[4] = "SHC in component SHCtoSHCStar (um)" legend_states[5] = "SHCstar in component SHCtoSHCStar (um)" legend_states[6] = "SHCstar_SOS_GRB2 in component SHCtoSHCStar (um)" legend_states[7] = "SOS_GRB2 in component SHCtoSHCStar (um)" legend_states[8] = "SOS in component SHCtoSHCStar (um)" legend_constants[20] = "GRB2 in component SHCtoSHCStar (um)" legend_constants[21] = "MAPK in component SHCtoSHCStar (um)" legend_states[9] = "SOSstar in component SHCtoSHCStar (um)" legend_states[10] = "SOSstar_GRB2 in component SHCtoSHCStar (um)" legend_constants[22] = "km7 in component GDPrasToGTPras (um)" legend_constants[23] = "Vmax7 in component GDPrasToGTPras (per_s)" legend_states[11] = "GDP_ras in component GDPrasToGTPras (um)" legend_states[12] = "GTP_ras in component GDPrasToGTPras (um)" legend_rates[0] = "d/dt EGF in component EGF_EGFRtoEGFEGFR (um)" legend_rates[1] = "d/dt EGFR in component EGF_EGFRtoEGFEGFR (um)" legend_rates[2] = "d/dt EGF_EGFR in component EGF_EGFRtoEGFEGFR (um)" legend_rates[3] = "d/dt EGF_EGFR_INTERNAL in component EGF_EGFRtoEGFEGFR (um)" legend_rates[5] = "d/dt SHCstar in component SHCtoSHCStar (um)" legend_rates[4] = "d/dt SHC in component SHCtoSHCStar (um)" legend_rates[6] = "d/dt SHCstar_SOS_GRB2 in component SHCtoSHCStar (um)" legend_rates[7] = "d/dt SOS_GRB2 in component SHCtoSHCStar (um)" legend_rates[8] = "d/dt SOS in component SHCtoSHCStar (um)" legend_rates[9] = "d/dt SOSstar in component SHCtoSHCStar (um)" legend_rates[10] = "d/dt SOSstar_GRB2 in component SHCtoSHCStar (um)" legend_rates[11] = "d/dt GDP_ras in component GDPrasToGTPras (um)" legend_rates[12] = "d/dt GTP_ras in component GDPrasToGTPras (um)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.000007 constants[1] = 0.25 constants[2] = 0.002 constants[3] = 0.00033 states[0] = 0.16667 states[1] = 0.16667 states[2] = 0 states[3] = 0 constants[4] = 0.83333333333 constants[5] = 0.0016667 constants[6] = 0 constants[7] = 0.000000041667 constants[8] = 0.0168 constants[9] = 0.0000008333 constants[10] = 0.1 constants[11] = 0.001 constants[12] = 0 constants[13] = 0.000000041667 constants[14] = 0.0168 constants[15] = 0.40404 constants[16] = 2.564166667 constants[17] = 0.02 constants[18] = 0.2 constants[19] = 10 states[4] = 0.5 states[5] = 0 states[6] = 0 states[7] = 0 states[8] = 0.1 constants[20] = 1 constants[21] = 0.36 states[9] = 0 states[10] = 0 constants[22] = 0.50505 constants[23] = 0.02 states[11] = 1 states[12] = 0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = -constants[0]*states[0]*states[1]+constants[1]*states[2] rates[1] = -constants[0]*states[0]*states[1]+constants[1]*states[2] rates[2] = ((constants[0]*states[0]*states[1]-constants[1]*states[2])-constants[2]*states[2])+constants[3]*states[3] rates[3] = constants[2]*states[2]-constants[3]*states[3] rates[5] = ((states[2]*constants[18]*states[4])/(constants[4]+states[4])-constants[9]*states[5]*states[7])+constants[10]*states[6] rates[4] = (constants[5]*states[5]-constants[6]*states[4])-(states[2]*constants[18]*states[4])/(constants[4]+states[4]) rates[6] = constants[9]*states[5]*states[7]-constants[10]*states[6] rates[7] = ((-constants[9]*states[5]*states[7]+constants[10]*states[6])-constants[8]*states[7])+constants[7]*states[8]*constants[20] rates[8] = (constants[11]*states[9]-constants[12]*states[8])-(constants[21]*constants[19]*states[8])/(constants[16]+states[8]) rates[9] = ((-constants[11]*states[9]+constants[12]*states[8]+(constants[21]*constants[19]*states[8])/(constants[16]+states[8]))-constants[13]*states[9]*constants[20])+constants[14]*states[10] rates[10] = constants[13]*states[9]*constants[20]-constants[14]*states[10] rates[11] = (-states[10]*constants[23]*states[11])/(constants[22]+states[11]) rates[12] = (states[10]*constants[23]*states[11])/(constants[22]+states[11]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) return algebraic def solve_model(): """Solve model with ODE solver""" from scipy.integrate import ode # Initialise constants and state variables (init_states, constants) = initConsts() # Set timespan to solve over voi = linspace(0, 10, 500) # Construct ODE object to solve r = ode(computeRates) r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1) r.set_initial_value(init_states, voi[0]) r.set_f_params(constants) # Solve model states = array([[0.0] * len(voi)] * sizeStates) states[:,0] = init_states for (i,t) in enumerate(voi[1:]): if r.successful(): r.integrate(t) states[:,i+1] = r.y else: break # Compute algebraic variables algebraic = computeAlgebraic(constants, states, voi) return (voi, states, algebraic) def plot_model(voi, states, algebraic): """Plot variables against variable of integration""" import pylab (legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends() pylab.figure(1) pylab.plot(voi,vstack((states,algebraic)).T) pylab.xlabel(legend_voi) pylab.legend(legend_states + legend_algebraic, loc='best') pylab.show() if __name__ == "__main__": (voi, states, algebraic) = solve_model() plot_model(voi, states, algebraic)